Many years ago I worked in a tire factory ( quality control ) ---Today I tell folks that ----" they are all black , but they are not all the same "------Today I say the same thing about impellers.------Put a new one in at least every 5 years.
I would say that the impeller / pumps are much misunderstood. -----They are critical for long motor life.----On most motors they should be replaced every 5 years.----And even more often in when running in cold water !
Some beepers have a wee circuit in them,----When power is applied they do a " self check " and then turn off.----That little " circuit " can be defective.----The faint tone can also mean a poor connection or a wire touching ground somewhere.